Deprojection of the r^1/4^ law tables

A spherical galaxy with reduced surface brightness, J=B({alpha})/B_e_, obeying the r^1/4^ law, logJ=-3.3307 ({alpha}^1/4^-1), where {alpha} is the reduced radius, {alpha}=r/r_e_ (r_e_ is the effective radius), is deprojected to find the corresponding space density, mass, mean density, force, potential, escape velocity, and potential energy at each point in the galaxy. Numerical tabulations to five significant figures are given for 124 points in the range 10^-6^<=R/r_e_<=260.

In addition the projected surface brightness B({alpha}) and integrated luminosity within {alpha} are tabulated for the range 10^-6^<={alpha}=r/r_e_<=260. Conversion factors to cgs units and to M_{sun}_, pc, km/s, L_{sun}_ units are given. Asymptotic expansions for the space density {rho}(s) in the ranges s=<10^-4^ and s>=10^-1^ are derived, and it is demonstrated that the projection of the expansion for s<=10^-1^ is almost indistinguishable from the r^1/4^ law itself, apart from a small excess of luminosity in the central regions.